CBSE Class 12-science Answered
pls solve
![question image](http://images.topperlearning.com/topper/new-ate/top_mob16740631162080843328IMG-20230118-WA0005.jpg)
Asked by sdmbotch1123 | 18 Jan, 2023, 23:01: PM
Let ![begin mathsize 14px style b with rightwards arrow on top space equals space alpha space i with hat on top space plus space beta space j with hat on top space plus space gamma space k with hat on top space end style](https://images.topperlearning.com/topper/tinymce/cache/66d18dda1a40276ca5380e5db73569ce.png)
![begin mathsize 14px style b with rightwards arrow on top space equals space alpha space i with hat on top space plus space beta space j with hat on top space plus space gamma space k with hat on top space end style](https://images.topperlearning.com/topper/tinymce/cache/66d18dda1a40276ca5380e5db73569ce.png)
![begin mathsize 14px style a with rightwards arrow on top space cross times space b with rightwards arrow on top space equals space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row 1 1 1 row alpha beta gamma end table close vertical bar space equals space open parentheses gamma minus beta close parentheses i with hat on top space plus open parentheses alpha minus gamma close parentheses j with hat on top space plus space open parentheses beta minus alpha close parentheses k with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/d1fa8d1f2f90a8f8d1a0609f5f4797f8.png)
We are given that
....................................... (2)
![begin mathsize 14px style a with rightwards arrow on top space cross times b with rightwards arrow on top space equals space j with hat on top space minus space k with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/92d0f2b65e765e9c5f7fd4608b749704.png)
By comparing eqn.(1) and eqn.(2) , we get
β = γ .............................. (3)
α - γ = 1 or γ = α - 1
β - α = -1 or β = α - 1
![begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top space equals space open parentheses space i with hat on top space plus space j with hat on top space plus space k with hat on top close parentheses space times space open parentheses alpha space i with hat on top space plus beta space j with hat on top space plus gamma space k with hat on top close parentheses space equals space alpha plus beta plus gamma end style](https://images.topperlearning.com/topper/tinymce/cache/5cd3f3e6119e923d1b94e1d357ebf58a.png)
we are given that ![begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top space equals space 3 end style](https://images.topperlearning.com/topper/tinymce/cache/6c8b73c7fef97d30acd7796279948478.png)
![begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top space equals space 3 end style](https://images.topperlearning.com/topper/tinymce/cache/6c8b73c7fef97d30acd7796279948478.png)
hence we get ![begin mathsize 14px style alpha space plus space beta space plus space gamma space equals space 3 end style](https://images.topperlearning.com/topper/tinymce/cache/ae500796fdf21025d6e68de4f342cd87.png)
![begin mathsize 14px style alpha space plus space beta space plus space gamma space equals space 3 end style](https://images.topperlearning.com/topper/tinymce/cache/ae500796fdf21025d6e68de4f342cd87.png)
α + ( α -1 ) + ( α -1 ) = 3 α -2 = 3
α = 5/3 ; β = α - 1 = (5/3) - 1 = (2/3) ; γ = β = (2/3)
Hence ![begin mathsize 14px style c with rightwards arrow on top space equals space 1 third open parentheses 5 space i with hat on top space plus space 2 j with hat on top space plus space 2 k with hat on top close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/d510a56be711b10ecb4e3523d03afe48.png)
![begin mathsize 14px style c with rightwards arrow on top space equals space 1 third open parentheses 5 space i with hat on top space plus space 2 j with hat on top space plus space 2 k with hat on top close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/d510a56be711b10ecb4e3523d03afe48.png)
![begin mathsize 14px style open vertical bar c with rightwards arrow on top close vertical bar space equals space 1 third open parentheses square root of 25 plus 4 plus 4 end root close parentheses space equals space square root of 33 over 9 end root space equals space square root of 11 over 3 end root end style](https://images.topperlearning.com/topper/tinymce/cache/86230316fef809e434d13595181c7b24.png)
Answered by Thiyagarajan K | 19 Jan, 2023, 00:17: AM
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